Question

A runner finishes a 200-meter dash in 35 seconds. Let r represent any speed (in meters per second) faster than the runner's speed. Write an inequality that represents r

Answer 1

Answer:

Part a) $r > \frac{40}{7}\ \frac{m}{sec}$ (the graph in the attached figure)

Part b) see the explanation                                        

Step-by-step explanation:

The complete question is

A runner finishes a 200-meter dash in  35 seconds. Let r represent any speed (in meters  per second) faster than the runner’s speed.

a. Write an inequality that represents r. Then graph  the inequality.

b. Every point on the graph represents a speed faster  than the runner’s speed. Do you think every point  could represent the speed of a runner?

Part a)

we know that                                      

The speed of the runner is equal to divide the distance by the time

so              

$\frac{200}{35}\ \frac{m}{sec}$                        

Simplify                      

$\frac{40}{7}\ \frac{m}{sec}$          

Let

r -----> represent any speed (in meters per second) faster than the runner's speed

The inequality that represent r is

$r > \frac{40}{7}\ \frac{m}{sec}$

using a graphing tool

The graph in the attached figure

The solution is all real numbers greater than 40/7 m/sec

Part b)

we know that

From a mathematical point of view, every point of the graph belong to the solution set , but from a practical point of view the runner's speed is physically limited, so the solution set is a boundary interval